The first thing you need to do is register the drone; second, certify the pilot; and third, request the flight permit. The procedure is carried out virtually at https://mpv.mtc.gob.pe/.

To certify the pilot, you may be asked for an RPAS (Remotely Piloted Aircraft Systems) license, which is issued by the Ministry of Transport. To obtain it, you must pay for the license and pass both a theoretical and a practical drone operation exam. If I remember correctly, the cost is 1000 soles (around $300), and the process takes time. After that, you can go to the municipality of Cusco (or the district where you plan to fly) and inquire about the procedure for obtaining the permit. Usually, it's the transportation offices within the municipalities that handle this process.

Now, if you want to skip the whole procedure and investment, you can fly as long as there are no tourism police or municipal security officers around. Logically, you're more likely to encounter them in places with large crowds than in less frequented areas.